WASHINGTON (Reuters) - The public may soon be able to delve into how a U.S. District Court judge came to rule that MetLife Inc <MET.N> is not "too big to fail," after three appeals judges on Tuesday decided many records in the case should be unsealed.

District Court Judge Rosemary Collyer last year rescinded financial regulators' designation of MetLife, the largest U.S. life insurer, as "systemically important," a label triggering heightened oversight and requirements to hold additional capital.

When advocacy group Better Markets then asked Collyer to unseal the case's records, she decided that under a confidentiality provision in the Dodd-Frank Wall Street reform law they had to remain under wraps.

Better Markets appealed that decision while former President Barack Obama, a Democrat, appealed Collyer's recission.

Both appeals were argued at the U.S. Court of Appeals for the District of Columbia. The three-judge panels hearing the appeals share one member, Judge Sri Srinivasan, an Obama appointee.

Tuesday's opinion in the Better Markets appeal was written by Chief Judge Merrick Garland, Obama's nominee to the U.S. Supreme Court who the Republican-led Senate last year refused to consider.

It said the public has a longstanding right to see judicial records.

"The right of public access is a fundamental element of the rule of law, important to maintaining the integrity and legitimacy of an independent judicial branch," the opinion said.

In a unanimous vote, the judges remanded the case, ordering the lower court to review each document and provide reasons beyond the Dodd-Frank provision for any it decides should remain sealed.

"The decision is a huge victory for the American people and their right to know how our courts and agencies are protecting the public interest," said Stephen Hall, the Better Markets legal director who had argued the appeal.

The Financial Stability Oversight Council, which includes the Treasury secretary, Securities and Exchange Commission chair and the Federal Reserve chair, was established within Dodd-Frank in part to identify institutions so large and interconnected they could devastate the financial system if they fail.

The council, which now includes many of Republican President Donald Trump's appointees, is currently considering whether it should withdraw Obama's appeal.

Many had expected the appeals judges to render a decision soon after hearing arguments in October. But since January, MetLife and FSOC have both asked for abeyances.